“Class” starts out on familiar ground: Characters run down a hallway, pursued by a nightmare creature. So far, so “Doctor Who” (which also returns the same night, and naturally involves its own hallway chase).

“Class,” a spinoff from the venerated sci-fi mothership currently starring Peter Capaldi, doesn’t stray all that far from the basic formula of the original. It’s got monsters, an unfortunate rip in the fabric of time and space, pop culture-obsessed characters who quip and banter, and an acerbic adult on hand to provide guidance and, on occasion, to skillfully exude irritation.

What “Class” doesn’t have yet is its very own reason to exist. It generally riffs on the kinds of plots and premises that have been “Doctor Who’s” stock in trade for decades, but on “Class,” those storylines feel a bit threadbare and padded.

In “Class,” the ratio of adult to young companions has been altered: Aboard “Doctor Who’s” TARDIS, in addition to the Doctor himself, there’s usually one companion — two is usually the maximum. In the spinoff, however, Miss Quill (Katherine Kelly) has four young people around her, all of whom are students at the Coal Hill Academy (a place that will be familiar to “Doctor Who” fans, given that several episodes in recent years have been set at a slightly different version of the school). Miss Quill, despite her status as a teacher at Coal Hill, isn’t much inclined to act as a mentor or friend, given that she’s a refugee from another planet who is locked into involuntary servitude to one of the other characters.

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Miss Quill is by far the best part of “Class”: She’s dreadfully unimpressed with Earth, schools, teenagers and her lot in life, and Katherine Kelly gives her frustration a great deal of subversive energy. The rest of the characters, unfortunately, are quite dull.

On paper, the Coal Hill students have the kinds of problems that should make them interesting, but “Class” fails to give the alien invasions, or the students’ romances and ongoing emotional dilemmas, the kind of consistent urgency they need to be watchable. Sitting through multiple episodes of “Class,” which are competent without being memorable, makes one wish that the CW had gotten the job of making a “Doctor Who” spinoff set at a high school. On that network, both the episodic plots and the characters’ relationships would gain traction with enjoyable efficiency, but on “Class,” a character who is the last of his race comes off as anything but tragic, and other traits and obstacles feel similarly perfunctory and predictable. There’s just not enough to grab on to for all but the most devoted “Doctor Who” completists.

Over on the TARDIS, big changes are afoot, and some of them also involve a student. Bill (Pearl Mackie), a young woman with a thirst for knowledge, joins the team in the TARDIS, and if the first episode of the new season — which is Capaldi’s last as the Doctor — is a bit of a greatest-hits rehash, that is easy to forgive.

Mackie is an energetic and enjoyable addition to the show, and her down-to-Earth character brings a healthy skepticism to all things Doctor-related. Even more charming than Bill’s curiosity and intelligence are her interactions with Nardole (Matt Lucas), the rather stolid but amusing character the Doctor came across in his recent travels across the galaxy. The “Doctor Who” season premiere is essentially a comedic romp across the galaxy, and with performers this skilled clearly having fun lobbing their dialogue back and forth, it’s hard to quibble with the the thin and literally watered-down nature of the plot. (There’s a water menace, it’s not worth explaining.)

With this trio in the TARDIS, “Doctor Who” looks set to give Capaldi a send-off season full of cheeky, lively chemistry, as long as the show stays away from the kind of overwrought, superficial and undernourished storytelling that it has peddled at times in recent years. (The show has been remarkably uneven in recent years, though Capaldi has been consistently outstanding.)

“Class” has more characters — five series regulars, to be exact — and yet the core “Doctor Who” trio is a more satisfying team. But somehow that seems appropriate for a show about a man who flies around in a blue box that is bigger on the inside; size isn’t everything.

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